Question

What is the explicit rule for this geometric sequence? a1=-15;an=1/5•an-1

Answer 1

A

Explanation:

A, all the way proof right here and I got 100% on the quiz

Answer 2

Option A is correct.

`a_n =-15 ((1)/(5))^(n-1)`

Explanation:

Given:
`a_1 = -15` ;
`a_n = (1)/(5) \cdot a_(n-1)`

for n = 2

`a_2 = (1)/(5) \cdot a_(2-1)` =
`(1)/(5)\cdot a_1 = (1)/(5) \cdot (-15)`

for n =3

`a_3 = (1)/(5) \cdot a_(3-1)` =
`(1)/(5) \cdota_2= ((1)/(5))^2\cdot (-15)`

Simlarly , for n =4

`a_3 = (1)/(5) \cdot a_(4-1)` =
`(1)/(5)\cdot a_3= ((1)/(5))^3\cdot (-15)`

and so on...

Common ratio(r) states that for a geometric sequence or geometric series, the common ratio is the ratio of a term to the previous term.

we have;
`r = (a_2)/(a_1) = (1)/(5)`

Now; by recursive formula for geometric series:

`a_n = a_1 r^(n-1)`

where
`a_1` is the first term and r is the common ratio:

Substitute the value of
`a_1 = -15` and
`r = (1)/(5)`

we have;

`a_n =-15 ((1)/(5))^(n-1)`

therefore, the explicit rule for the geometric sequence is;
`a_n =-15 ((1)/(5))^(n-1)`